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 A117724 Triangle T(n,k) = coefficient [x^n] of x^2/(1-(k+1)*x^2-x^3) for row n, and columns k = 0..n, read by rows. 2
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 4, 9, 16, 25, 36, 49, 2, 4, 6, 8, 10, 12, 14, 16, 2, 9, 28, 65, 126, 217, 344, 513, 730, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 4, 22, 90, 268, 640, 1314, 2422, 4120, 6588, 10030, 14674 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Nathaniel Johnston, Rows n = 0..50, flattened FORMULA T(n,k) = coefficient [x^n] ( x^2/(1-(k+1)*x^2-x^3) ). T(n, 0) = A000931(n+1). T(n, 1) = A008346(n-2) = (-1)^(n-1)*A119282(n-1). T(n, 2) = A052931(n-2). EXAMPLE The table starts: 0; 0, 0; 1, 1, 1; 0, 0, 0, 0; 1, 2, 3, 4, 5; 1, 1, 1, 1, 1, 1; 1, 4, 9, 16, 25, 36, 49; 2, 4, 6, 8, 10, 12, 14, 16; 2, 9, 28, 65, 126, 217, 344, 513, 730; 3, 12, 27, 48, 75, 108, 147, 192, 243, 300; MAPLE t:=taylor(x^2/(1-(k+1)*x^2-x^3), x, 15): seq(seq(coeff(t, x, n), k=0..n), n=0..12); # Nathaniel Johnston, Apr 27 2011 MATHEMATICA T[n_, k_]:= T[n, k]= Coefficient[Series[x^2/(1-(k+1)*x^2-x^3), {x, 0, n+ 2}], x, n]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten PROG (Magma) m:=12; R:=PowerSeriesRing(Integers(), m+2); A117724:= func< n, k | Coefficient(R!( x^2/(1-(k+1)*x^2-x^3) ), n) >; [A117724(n, k): k in [0..n], n in [0..m]]; // G. C. Greubel, Jul 23 2023 (SageMath) def A117724(n, k): P. = PowerSeriesRing(QQ) return P( x^2/(1-(k+1)*x^2-x^3) ).list()[n] flatten([[A117724(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 23 2023 CROSSREFS Cf. A000931, A008346, A052931, A117716, A119282. Sequence in context: A256306 A030548 A346690 * A255826 A339256 A277544 Adjacent sequences: A117721 A117722 A117723 * A117725 A117726 A117727 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Apr 13 2006 EXTENSIONS Sign in definition corrected, offset set to -1 by Assoc. Eds. of the OEIS, Jun 15 2010 Edited by G. C. Greubel, Jul 23 2023 STATUS approved

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Last modified June 19 09:37 EDT 2024. Contains 373501 sequences. (Running on oeis4.)